Planck data have been used to provide stringent new constraints on
cosmic strings and other defects. We describe forecasts of the CMB power
spectrum induced by cosmic strings, calculating these from network
models and simulations using line-of-sight Boltzmann solvers. We have
studied Nambu-Goto cosmic strings, as well as field theory strings for
which radiative effects are important, thus spanning the range of
theoretical uncertainty in the underlying strings models. We have added
the angular power spectrum from strings to that for a simple adiabatic
model, with the extra fraction defined as f<SUB>10</SUB> at multipole
l = 10. This parameter has been added to the standard six parameter
fit using COSMOMC with flat priors. For the Nambu-Goto string model, we
have obtained a constraint on the string tension of Gmu/c<SUP>2</SUP>
< 1.5 � 10<SUP>-7</SUP> and f<SUB>10</SUB> < 0.015 at 95%
confidence that can be improved to Gmu/c<SUP>2</SUP> < 1.3 �
10<SUP>-7</SUP> and f<SUB>10</SUB> < 0.010 on inclusion of high-l
CMB data. For the Abelian-Higgs field theory model we find,
Gmu<SUB>AH</SUB>/c<SUP>2</SUP>< 3.2 � 10<SUP>-7</SUP> and
f<SUB>10</SUB> < 0.028. The marginalised likelihoods for
f<SUB>10</SUB> and in the
f<SUB>10</SUB>-Omega<SUB>b</SUB>h<SUP>2</SUP> plane are also
presented. We have additionally obtained comparable constraints on
f<SUB>10</SUB> for models with semilocal strings and global textures. In
terms of the effective defect energy scale these are somewhat weaker at
Gmu/c<SUP>2</SUP> < 1.1 � 10<SUP>-6</SUP>. We have made
complementarity searches for the specific non-Gaussian signatures of
cosmic strings, calibrating with all-sky Planck resolution CMB maps
generated from networks of post-recombination strings. We have validated
our non-Gaussian searches using these simulated maps in a
Planck-realistic context, estimating sensitivities of up to
DeltaGmu/c<SUP>2</SUP> &ap; 4 � 10<SUP>-7</SUP>. We have
obtained upper limits on the string tension at 95% confidence of
Gmu/c<SUP>2</SUP> < 9.0 � 10<SUP>-7</SUP> with modal
bispectrum estimation and Gmu/c<SUP>2</SUP> < 7.8 �
10<SUP>-7</SUP> for real space searches with Minkowski functionals.
These are conservative upper bounds because only post-recombination
string contributions have been included in the non-Gaussian analysis.

Planck data have been used to provide stringent new constraints on
cosmic strings and other defects. We describe forecasts of the CMB power
spectrum induced by cosmic strings, calculating these from network
models and simulations using line-of-sight Boltzmann solvers. We have
studied Nambu-Goto cosmic strings, as well as field theory strings for
which radiative effects are important, thus spanning the range of
theoretical uncertainty in the underlying strings models. We have added
the angular power spectrum from strings to that for a simple adiabatic
model, with the extra fraction defined as f<SUB>10</SUB> at multipole
l = 10. This parameter has been added to the standard six parameter
fit using COSMOMC with flat priors. For the Nambu-Goto string model, we
have obtained a constraint on the string tension of Gmu/c<SUP>2</SUP>
< 1.5 � 10<SUP>-7</SUP> and f<SUB>10</SUB> < 0.015 at 95%
confidence that can be improved to Gmu/c<SUP>2</SUP> < 1.3 �
10<SUP>-7</SUP> and f<SUB>10</SUB> < 0.010 on inclusion of high-l
CMB data. For the Abelian-Higgs field theory model we find,
Gmu<SUB>AH</SUB>/c<SUP>2</SUP>< 3.2 � 10<SUP>-7</SUP> and
f<SUB>10</SUB> < 0.028. The marginalised likelihoods for
f<SUB>10</SUB> and in the
f<SUB>10</SUB>-Omega<SUB>b</SUB>h<SUP>2</SUP> plane are also
presented. We have additionally obtained comparable constraints on
f<SUB>10</SUB> for models with semilocal strings and global textures. In
terms of the effective defect energy scale these are somewhat weaker at
Gmu/c<SUP>2</SUP> < 1.1 � 10<SUP>-6</SUP>. We have made
complementarity searches for the specific non-Gaussian signatures of
cosmic strings, calibrating with all-sky Planck resolution CMB maps
generated from networks of post-recombination strings. We have validated
our non-Gaussian searches using these simulated maps in a
Planck-realistic context, estimating sensitivities of up to
DeltaGmu/c<SUP>2</SUP> &ap; 4 � 10<SUP>-7</SUP>. We have
obtained upper limits on the string tension at 95% confidence of
Gmu/c<SUP>2</SUP> < 9.0 � 10<SUP>-7</SUP> with modal
bispectrum estimation and Gmu/c<SUP>2</SUP> < 7.8 �
10<SUP>-7</SUP> for real space searches with Minkowski functionals.
These are conservative upper bounds because only post-recombination
string contributions have been included in the non-Gaussian analysis.